Shanghai 1990-2010 · Before and after the great construction explosion at the turn of the 21st Century.
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The exponential construction trend in Shanghai over the past two decades brings a simple question to mind. What laws govern the growth dynamics of cities? All seem to be marked by an explosive period of growth, often followed by a plateau and a slight shrinking. The explosive period necessarily aligns with an economic or territorial supremacy (for London this is 1850-1910, see below) - this is as true of Athens and Rome as it is of modern China.

Spatial interaction models posit a range of suggestions for a mathematical treatment of urban-scale growth. Wilson’s work utilises Lotka-Volterra dynamics, which are ‘borrowed’ from ecology, as they were first used to describe population dynamics in prey-predator systems. May’s equation expands on L-V, introducing logistic growth constrained via a carrying capacity. These produce a complex dynamics with multiple equilibria, and, within BLV models, have been shown to provide a good fit for the slow evolution of urban space.

Urban Planet · Distribution of urban population growth around the world (showing the rise of the global south) · Urban Age (2009)
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Modernity could be defined as a singularity which takes us out of growth cycles — cities periodically growing and diminishing with disease or disaster — and into an uncharted terrain where limits to growth relate to planetary resources. Through modern history, the time taken for the world population to double has roughly halved each time - hyperbolic growth. By taking a step back, we see the global dynamics behind increasingly intensified urbanisation.

At this moment, singularity is a scenario for world population growth, but it’s sensible to assume the Earth’s carrying capacity constraints will start to be felt in the near future. This scenario reins in a singularity, suggesting instead that our current period of urbanisation — what Soja would call the ‘third wave’ — will produce a phase transition in urban population which stabilises in the decades to come. The third scenario is a catastrophe, although the UN is in denial about this - official world population projections only admit scenarios a) and b), with the low scenario represented by a gentle curve. A catastrophe would imply a steep collapse in world population.